Problem: Simplify the following expression: $ p = \dfrac{x - 9}{6} + \dfrac{8}{3} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{x - 9}{6} \times \dfrac{3}{3} = \dfrac{3x - 27}{18} $ Multiply the second expression by $\dfrac{6}{6}$ $ \dfrac{8}{3} \times \dfrac{6}{6} = \dfrac{48}{18} $ Therefore $ p = \dfrac{3x - 27}{18} + \dfrac{48}{18} $ Now the expressions have the same denominator we can simply add the numerators: $p = \dfrac{3x - 27 + 48}{18} $ $p = \dfrac{3x + 21}{18}$ Simplify the expression by dividing the numerator and denominator by 3: $p = \dfrac{x + 7}{6}$